
rum
around
Colloquial short form of 'herum' (around); expresses movement around something or in a circle.
Wir sind eine Stunde im Park rumgelaufen.
We walked around in the park for an hour.
around / over
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around
Colloquial short form of 'herum' (around); expresses movement around something or in a circle.
Wir sind eine Stunde im Park rumgelaufen.
We walked around in the park for an hour.

over
Colloquial for 'vorbei' (over/past) or 'zu Ende' (finished), often in reference to time.
Das Wochenende ist schon wieder rum.
The weekend is already over again.

around
Colloquial for 'ungefähr' (approximately) or 'etwa' (about), usually in connection with a time or quantity.
Ich bin so gegen 18 Uhr rum zu Hause.
I'll be home at around 6 p.m.

around
Colloquial, used to describe an aimless or inactive action, often with a slightly negative connotation.
Steh nicht so dumm rum, sondern hilf mir!
Don't just stand around looking stupid—help me!
'Rum' is the colloquial short form of 'herum' (around). It is used almost exclusively in spoken language or in informal texts.
Lass uns noch eine Runde im Park rumgehen.
Let's walk around the park for another loop.
'Rum' is very often used as a separable part of verbs to describe an aimless, undefined, or repeated action. Examples include 'rumlaufen' (to walk/run around), 'rumsitzen' (to sit around), or 'rumliegen' (to lie around).
Die Kinder laufen den ganzen Tag im Garten rum.
The children run around in the garden all day.
In the meaning of 'vorbei' (over/past) or 'zu Ende' (finished), 'rum' is almost always used with units of time. Typical phrases are 'das Wochenende ist rum' (the weekend is over) or 'die Ferien sind rum' (the holidays are over).
Kaum hat der Urlaub angefangen, schon ist er wieder rum.
No sooner has the vacation started than it's already over again.
When 'rum' means 'ungefähr' (approximately), it usually comes after the time or quantity. It is often combined with words like 'so' (about) or 'gegen' (around).
Wir treffen uns so um sieben rum.
We'll meet at around seven.
In combinations like 'rumstehen' (to stand around) or 'rumliegen' (to lie around), 'rum' often has a slightly negative meaning. It implies that someone or something is useless or in the way.
Lass deine schmutzigen Socken nicht überall rumliegen!
Don't leave your dirty socks lying around everywhere!
at / around / in order to
Um and rum can both indicate an approximate time or amount. Um is the neutral standard form and functions as a preposition in the expression, while rum is colloquial and occurs especially in spoken language. Use um in neutral texts and rum in casual conversations.

Die Reparatur kostet rum zweihundert Euro.
The repair costs around two hundred euros.
Die Reparatur kostet um die zweihundert Euro.
The repair costs around two hundred euros.